Exercise 24.6.3 Assume in a period that the bond price can go from $1 to Pu or Pd and that the value of a derivative can go from $1 to Vu or Vd. (1) Show that a portfolio of $1 worth of bonds and (Pd − Pu)/(Vu −Vd) units of the derivative is riskless. (2) Prove that these many derivatives are worth

(R− Pd) Vu +(Pu − R) Vd

(Pu − Pd) R in total, where R≡ 1+r is the gross riskless return.